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\begin{patch}{QuaternionXmpPagePatch1}
\begin{paste}{QuaternionXmpPageFull1}{QuaternionXmpPageEmpty1}
\pastebutton{QuaternionXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{q := quatern(2/11,-8,3/4,1)\bound{q }}
\indentrel{3}\begin{verbatim}
2 3
(1) �� - 8i + � j + k
11 4
Type: Quaternion Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPageEmpty1}
\begin{paste}{QuaternionXmpPageEmpty1}{QuaternionXmpPagePatch1}
\pastebutton{QuaternionXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{q := quatern(2/11,-8,3/4,1)\bound{q }}
\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPagePatch2}
\begin{paste}{QuaternionXmpPageFull2}{QuaternionXmpPageEmpty2}
\pastebutton{QuaternionXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{[real q, imagI q, imagJ q, imagK q]\free{q }}
\indentrel{3}\begin{verbatim}
2 3
(2) [��,- 8,�,1]
11 4
Type: List Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPageEmpty2}
\begin{paste}{QuaternionXmpPageEmpty2}{QuaternionXmpPagePatch2}
\pastebutton{QuaternionXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{[real q, imagI q, imagJ q, imagK q]\free{q }}
\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPagePatch3}
\begin{paste}{QuaternionXmpPageFull3}{QuaternionXmpPageEmpty3}
\pastebutton{QuaternionXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{inv q\free{q }}
\indentrel{3}\begin{verbatim}
352 15488 484 1936
(3) ������ + ������ i - ����� j - ������ k
126993 126993 42331 126993
Type: Quaternion Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPageEmpty3}
\begin{paste}{QuaternionXmpPageEmpty3}{QuaternionXmpPagePatch3}
\pastebutton{QuaternionXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{inv q\free{q }}
\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPagePatch4}
\begin{paste}{QuaternionXmpPageFull4}{QuaternionXmpPageEmpty4}
\pastebutton{QuaternionXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{q**6\free{q }}
\indentrel{3}\begin{verbatim}
(4)
2029490709319345 48251690851 144755072553
- ���������������� - ����������� i + ������������ j
7256313856 1288408 41229056
+
48251690851
����������� k
10307264
Type: Quaternion Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPageEmpty4}
\begin{paste}{QuaternionXmpPageEmpty4}{QuaternionXmpPagePatch4}
\pastebutton{QuaternionXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{q**6\free{q }}
\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPagePatch5}
\begin{paste}{QuaternionXmpPageFull5}{QuaternionXmpPageEmpty5}
\pastebutton{QuaternionXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{r := quatern(-2,3,23/9,-89); q + r\bound{r }\free{q }}
\indentrel{3}\begin{verbatim}
20 119
(5) - �� - 5i + ��� j - 88k
11 36
Type: Quaternion Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPageEmpty5}
\begin{paste}{QuaternionXmpPageEmpty5}{QuaternionXmpPagePatch5}
\pastebutton{QuaternionXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{r := quatern(-2,3,23/9,-89); q + r\bound{r }\free{q }}
\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPagePatch6}
\begin{paste}{QuaternionXmpPageFull6}{QuaternionXmpPageEmpty6}
\pastebutton{QuaternionXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{q * r - r * q\free{q r }}
\indentrel{3}\begin{verbatim}
2495 817
(6) - ���� i - 1418j - ��� k
18 18
Type: Quaternion Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPageEmpty6}
\begin{paste}{QuaternionXmpPageEmpty6}{QuaternionXmpPagePatch6}
\pastebutton{QuaternionXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{q * r - r * q\free{q r }}
\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPagePatch7}
\begin{paste}{QuaternionXmpPageFull7}{QuaternionXmpPageEmpty7}
\pastebutton{QuaternionXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{i:=quatern(0,1,0,0); j:=quatern(0,0,1,0); k:=quatern(0,0,0,1)\bound{i j k }}
\indentrel{3}\begin{verbatim}
(7) k
Type: Quaternion Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPageEmpty7}
\begin{paste}{QuaternionXmpPageEmpty7}{QuaternionXmpPagePatch7}
\pastebutton{QuaternionXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{i:=quatern(0,1,0,0); j:=quatern(0,0,1,0); k:=quatern(0,0,0,1)\bound{i j k }}
\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPagePatch8}
\begin{paste}{QuaternionXmpPageFull8}{QuaternionXmpPageEmpty8}
\pastebutton{QuaternionXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{[i*i, j*j, k*k, i*j, j*k, k*i, q*i]\free{i j k q }}
\indentrel{3}\begin{verbatim}
2 3
(8) [- 1,- 1,- 1,k,i,j,8 + �� i + j - � k]
11 4
Type: List Quaternion Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPageEmpty8}
\begin{paste}{QuaternionXmpPageEmpty8}{QuaternionXmpPagePatch8}
\pastebutton{QuaternionXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{[i*i, j*j, k*k, i*j, j*k, k*i, q*i]\free{i j k q }}
\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPagePatch9}
\begin{paste}{QuaternionXmpPageFull9}{QuaternionXmpPageEmpty9}
\pastebutton{QuaternionXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{norm q\free{q }}
\indentrel{3}\begin{verbatim}
126993
(9) ������
1936
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPageEmpty9}
\begin{paste}{QuaternionXmpPageEmpty9}{QuaternionXmpPagePatch9}
\pastebutton{QuaternionXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{norm q\free{q }}
\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPagePatch10}
\begin{paste}{QuaternionXmpPageFull10}{QuaternionXmpPageEmpty10}
\pastebutton{QuaternionXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{conjugate q\free{q }\bound{prev }}
\indentrel{3}\begin{verbatim}
2 3
(10) �� + 8i - � j - k
11 4
Type: Quaternion Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPageEmpty10}
\begin{paste}{QuaternionXmpPageEmpty10}{QuaternionXmpPagePatch10}
\pastebutton{QuaternionXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{conjugate q\free{q }\bound{prev }}
\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPagePatch11}
\begin{paste}{QuaternionXmpPageFull11}{QuaternionXmpPageEmpty11}
\pastebutton{QuaternionXmpPageFull11}{\hidepaste}
\tab{5}\spadcommand{q * \%\free{q prev }}
\indentrel{3}\begin{verbatim}
126993
(11) ������
1936
Type: Quaternion Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{QuaternionXmpPageEmpty11}
\begin{paste}{QuaternionXmpPageEmpty11}{QuaternionXmpPagePatch11}
\pastebutton{QuaternionXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{q * \%\free{q prev }}
\end{paste}\end{patch}
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